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Find the sum of the following series : ...

Find the sum of the following series : ` (1)/(4) + (1)/(2) + 1 + …` to n terms

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To find the sum of the series \( \frac{1}{4} + \frac{1}{2} + 1 + \ldots \) up to \( n \) terms, we can follow these steps: ### Step 1: Identify the Series The given series is: \[ \frac{1}{4} + \frac{1}{2} + 1 + \ldots \] We can rewrite the terms to see a pattern: ...
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AAKASH INSTITUTE ENGLISH-SEQUENCES AND SERIES -Try Yourself
  1. The sum of four numbers in G.P is 60 and the arithmetic mean of the ...

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  2. Find the sum of indicated number of terms of each of the following G.P...

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  3. Find the sum of the following series : (1)/(4) + (1)/(2) + 1 + … to...

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  4. Find the sum of indicated terms of each of the following geometric pro...

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  5. Find the sum to n terms (i) 9 + 99 + 999 + … (ii) 0.2 + 0.22...

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  6. How many terms of the series 1+2+2^2+….. must be taken to make 511?

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  7. A bag contains a total of 20 books on physics and mathematics, Any po...

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  8. Find the sum to infinity of the following G.P. (i) 1, (1)/(3) , (1)/...

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  9. Find the sum of the following series , (i) 0.5 + 0.05 + 0.005 + 0...

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  10. Prove that (9^(1/3).9^(1/9).9^(1/27)............oo)=3

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  11. Show that 9^(1/(4)).9^(1/(8)).9^(1/(16).) . .."to" oo = 3

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  12. The sum of an infinite G.P. . Is 6 and its first term is 2 . Find the ...

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  13. If the common ratio is -4/5 and the sum of infinite terms in a G.P is ...

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  14. Represent the following as rational numbers : (i) 0.bar(8)5 " " (...

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  15. Represent the following as rational numbers : (i) 0.bar15 " " (ii)...

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  16. If a, b, c , d are in G.P. , then shown that (i) (a + b)^(2) , (b ...

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  17. If a, b, c are in G.P. , then show that (i) (a^(2) - b^(2))(b^(2)...

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  18. Find the G.M. between the numbers. (i) 6 and 216 " " (ii...

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  19. Find the G.P. between the numbers . 1 and (4)/(25) " " ...

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  20. Insert four number between 6 and 192 so that the resulting sequence is...

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